Hi @TheSimpliFire

hello @OmegaKrypton

@MrPie wanna try this?]

@TheSimpliFire

@OmegaKrypton okey

Overthinking Monkey Enjoying Games And/ Awesome Knowledge Regarding Your Puzzles Today On Net

wow

progress^

@OmegaKrypton there are two "z" on the RHS and not LHS

That's why it's tricky

hmmm

BECAUSE NOBODY USES Z IN AUSTRALIA

Also 'v' on LHS but not on right

@MrPie So you say pussles :P

and lets get rid of "puzzles"

oops, that's a bit too close to something else ;)

I have: Overthinking Maddening Experimentalist Getting Awesome ~ Knowledge Regarding Y P T O N ..... ?

lol

Perplexing?

Paradox?

@OmegaKrypton maybe the second one

Nup, no spare D

First we have pussles

And now we have the D

maddened?

@OmegaKrypton that solves that problem

Now we need a spare O ....

I was thinking replacing "getting" with "good" or "godly" but then "awesome" doesn't work

Overthinking Maddened Experimentalist Getting Awesome ~ Knowledge Regarding Y Paradoxes T O N ..... ?

@OmegaKrypton there is an extra O on the RHS

Oh, @TheSimpliFire! I have exciting news!

yes?

what is it :)

@OmegaKrypton basically, @TheSimpliFire made a conjecture that $n^2=p+qr$ for all natural numbers $n>2$ where $p,q,r$ were primes and $q,r<n$.

yes

?

Let $n=2a$ for some $a\in\mathbf{N}_{>1}$ so that $4a^2=p+qr$. If $p=2$, then either $q$ or $r$ must equal $2$. Suppose it is $q$, then $2a^2=1+r\Leftrightarrow r=2a^2-1=2a^2-2+1=2(a+1)(a-1)+1$. Clearly, $(a+1)(a-1)$ is composite for $a>2$.

I noticed that the equation in particular, $r=2a^2-1$, obeys a negative pell equation

namely $$x^2-2y^2=-1.$$

what is that lol

@OmegaKrypton it is basically an equation with $x$ and $y$ where there are infinitely many solutions, and they are given by a recurrence relation

Do you know what that is?

What grants $r=x^2$?

@TheSimpliFire well, of course $r\neq x^2$ since $r$ is prime

... nvm

So that means $a\neq y$

just tell him the news

lol

@MrPie Exactly, so $x^2-2y^2$ cannot exist in terms of $r$

@OmegaKrypton I feel bad... ah well

@TheSimpliFire I wrote it in the paper

What you're doing is comparing $r-2a^2=-1$ to $x^2-2y^2=-1$ which isn't possible as $r$ can't be a square number

unless I'm mistaken

@TheSimpliFire but that's the point.

We can see what values $r$ cannot be

Fo example, $2*5^2-1=7^2$

therefore $r\neq 7$..... wait.... hold up

Actually, I'll start reading it after my exam as it's in an hour's time :P

@TheSimpliFire I got confused with $r$ and $a$

And it stuffed me up - badly

garyau @TheSimpliFire

:)

@OmegaKrypton DONE! :D

I am sure you can understand this

?

Basically, regarding that conjecture

If $n^2=p+qr$ and $n$ is even, then this means at least one of $p,q,r$ is even

Of course, that means at least one of them is $2$

If $p=2$, then one of $q$ or $r$ equals $2$. Suppose it is $q$.

so p,q,and r are primes?

yeah.

I can prove that if $n=2a$ for some natural number $a>1$ (greater than $1$ because $n>2$), then there are certain values that $a$ can never equal if $p=q=2$.

what if odd+odd = even>

?

@OmegaKrypton that's the second case where $p\neq 2$ and $q,r\neq 2$

ok

Oh yeah, I didn't explain myself clearly

@OmegaKrypton thanks :)

@TheSimpliFire I think I also proved that if $q=2$ then $r\equiv 1\pmod 3$

Nope, I didn't

there is a counter-example: $5^2=19+2\times 3$

Notice in that example, $q+r=n$.... hmmm....

Oh wait, $q,r>3$

Ah that make sense. I think this is true iff $q,r>3$

No actually. I let $r\ge q>3$ and got that $r\equiv 2\pmod 3$.

Overthinking Maddened Experimentalist Getting Awesome ~ Knowledge Regarding Y Paradoxes T O N ..... ?

any ideas? @MrPie @TheSimpliFire

senpais pls help...

@TheSimpliFire are u there?

yes

im bored

working on cryptics lol

wanna post a q soon

how bout you?

heh

@OmegaKrypton just finished my physics exam

it was alright

anymore coming?

In two weeks (3 more)

Until 7th June

garyau!

mine starts at beginning of june

:) It feels like I've had exams nonstop

sad...

keep optimistic lel :)

yup

@OmegaKrypton What exams do you have?

a lot...

like, what subjects?

chinese english math

liberal studies

science

history

chinese history

geography

Indeed that's a lot!

yep...

Over the past two weeks I had English, French, maths, physics chemistry and biology